I answer the above question in the light of two new elements. Firstly, in the 15th century while Cusanus did not practice experimental science, he substantially anticipated both the Copernican revolution and the birth of Galilei’s methodology. Secondly, I shall introduce a new conception of the foundations of modern science which are constituted by three dialectics. In this light, the complete birth of modern science, whose scope was so broad, required a very long historical process, which was completed in recent years. Within this long time span, Galileo was not only the first to practice a scientific methodology, but also almost the only scientist ever to be aware of the intellectual breadth of scientific enterprise.

8 Conclusion: What is Galileo’s role in this centuries long historical process?

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1 Introduction: What are the foundations of science? The three dialectics

The role played by Galileo in the birth of modern science depends on two questions: What is the definition of modern science, in particular its foundations? How long was the process of birth of modern science? Without doubt, the foundations of science are constituted by the well-known dialectic between experimental data and mathematical hypothesis. But after that, what in precise terms?

I suggest the following definition of the foundations of science that I obtained on the basis of four decades of historical works on the main theories of logic, mathematics and physics; they are constituted by two more dialectics of a theoretical nature; one between the two kinds of infinity (either potential, or actual) and a dialectic between the two types of organization of a theory (either deductive form principles-axioms, as Aristotle theorized in ancient times, AO, or aimed at the solution of a crucial problem, PO). The i...